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Consensus-based Distributed Estimation in Camera Networks
- A. T. Kamal, J. A. Farrell, A. K. Roy-ChowdhuryUniversity of California, Riverside
-akamal@ee.ucr.edu
ICIP 2012
Contents
• Problem Statement• Motivation for using Distributed Schemes• Challenges in Distributed Estimation in Camera
Networks• Our solution• Results
Problem Statement
Our goal is to estimate the state of the targets using the observations from all the cameras in a distributed manner.
C1C5
C3C2 C4
T1
T4
T3
T5
T2
Motivation for using Distributed Schemes
Issues using centralized or fully connected architectures:• High communication & processing power
requirements.• Intolerant of node failure.• Complicated to install.
Centralized
Partially connectedFully connected
Network architectures for multi-camera fusion
• Distributed schemes are scalable for any given connected network
Sensing Model
𝑥 𝑗,
𝐶 𝑖
𝒛 𝑖𝑗=𝑯𝑖
𝑗 𝒙 𝑗+𝝂 𝑖𝑗
Sending Model:
Parameter Vector: can be position, pose, appearance feature etc. of a target
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2
3
4
5
4 1.5
3.5
3.5
2.5
… 3
… 3
… 3
… 3
... 3
Average Consensus: Review
Average Consensus Algorithm
Example of Average Consensus
𝑧1=¿
𝑧 2=¿
𝑧 3=¿𝑧 4=¿
𝑧5=¿
𝑧𝑖 (𝑘+1 )=𝑧𝑖 (𝑘 )+𝜖 ∑𝑗∈𝒩𝑖
(𝑧 𝑗 (𝑘 )−𝑧𝑖 (𝑘))
lim𝑘→∞
𝑧 𝑖(𝑘)=∑𝑗=1
𝑁
𝑧 𝑗 (0)
𝑁
Each nodes converges to the global average
R. Olfati-saber, J. A. Fax, and R. J. Murray, “Consensus and cooperation in networked multi-agent systems,” in Proceedings of the IEEE, 2007
𝑓𝑜𝑟 𝑘=0 :∞
𝑒𝑛𝑑
Challenges in Distributed Estimation in Camera Networks
C1 C5
C3C2C4
T1
Challenges:• Each node may not observe the target
(i.e. difference between vision graph and comm. graph)
• The quality (noise variance) of measurementsat different nodes may be different.
• Network sparsity makes the above challenges severe.
We propose a distributed estimation framework which:• Does not require the knowledge of the vision
graph.• Weights measurements by noise variances.• Network sparsity does not affect the estimate it
converges to.
Distributed Maximum Likelihood Estimation (DMLE)
𝑥 (𝑘)𝑧𝑖 ,𝑅 𝑖
𝐶𝑖
𝑦 𝑖(0) ,𝑊 𝑖 (0)
𝑦 𝑛(0) ,𝑊𝑛 (0)
𝑦𝑚(0) ,𝑊𝑚(0)�̂�𝑖❑ ,𝐶𝑜𝑣 ( �̂� 𝑖
❑)
𝐶𝑚
𝐶𝑛
Information MatrixWeighted Measurement
𝑦 𝑖(1) ,𝑊 𝑖(1)
How is does DMLE solve the challenges?
• Weighted-average consensus
• Converges to the optimal ML estimate
(not affected by network sparsity.)
• Presence/absence and quality of measurement is captured in .(, for no node measurement)
Experimental Evaluation
C1C5
C3C2 C4
Error StatisticsGround TruthObservationsAvg. ConsensusDMLE
Legend:
**
Conclusion
This work was partially supported by ONR award N00014091066 titledDistributed Dynamic Scene Analysis in a Self-Configuring Multimodal Sensor Network.
• We have proposed a distributed parameter estimation method generalized for• Limited observability of nodes• Variable quality of measurements and• Network sparsity
that approaches the performance of the optimal centralized MLE.
• Future Work: Dynamic State Estimation (Distributed Kalman Filtering)
Incorporation of prior information and state dynamics (“Information Weighted Consensus - IEEE Decision and Control Conference, Dec 2012”)
Thank you
http://www.ee.ucr.edu/~akamal/
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